How do you multiply polynomials #(a + 3)(a - 2)#?

Question

Eli Assouline · Accepted Answer

#a^2+a-6#

#a*a=a^2#

#a*-2=-2a#

#3*a=3a#

#3*-2=-6#

Now when we combine them all together we get:

#a^2-2a+3a-6#

We still need to simplify this since #-2a# and #3a# are like terms. So the final answer is: #a^2+a-6#

Hope this helps!

Hazel Anglin · Answer

#a^2+a-6# #"each term in the second factor is multiplied by each"# #"term in the first factor"# #rArr(color(red)(a+3))(a-2)# #=color(red)(a)(a-2)color(red)(+3)(a-2)larrcolor(blue)"distribute"# #=(color(red)(a)xxa)+(color(red)(a)xx-2)+(color(red)(3)xxa)+(color(red)(3)xx-2)# #=a^2color(blue)(-2a)color(blue)(+3a)-6larrcolor(blue)"collect like terms"# #=a^2color(blue)(+a)-6# #rArr(a+3)(a-2)=a^2+a-6#

Abigail Allen · Answer

undefined To multiply polynomials (a + 3)(a - 2), you can use the distributive property or the FOIL method.

Distributive property:
(a + 3)(a - 2) = a(a) + a(-2) + 3(a) + 3(-2)
= a^2 - 2a + 3a - 6
= a^2 + a - 6

FOIL method:
(a + 3)(a - 2) = a*a + a*(-2) + 3*a + 3*(-2)
= a^2 - 2a + 3a - 6
= a^2 + a - 6